Caroline Kennedy's spokesman, Stefan Friedman, declined to comment.
The decision follows speculation that she was interested in the Senate seat that would become open if Clinton is confirmed as President-elect Barack Obama's next secretary of state.
If that happens, New York Gov. David Paterson would appoint someone to the seat for a two-year period, after which they would have to run for election, and, if they won, run for re-election again in 2012.
The governor has weeks to decide.
New York's senior senator, Charles Schumer, said he has also talked to Caroline Kennedy about the job.
"And she's clearly interested," he said.
Kennedy is the daughter of the late President John F. Kennedy. Her uncle, the late Robert F. Kennedy, once held the Senate seat she wants. Paterson has sole authority to name a replacement for Clinton, who was first elected in 2000 and re-elected by a wide margin in 2006.
Over the past week, Kennedy, who lives in Manhattan, has reached out to several prominent New York Democrats to tell them of her interest in the Senate seat. They included Joel Klein, chancellor of the New York City Department of Education. Kennedy worked closely with Klein as executive of the Office of Strategic Partnerships for the New York City Department of Education, where she raised about $65 million for the city's schools.
"I think she's thought about it a long time," Klein said of a conversation he had with Kennedy on Monday. He said the campaigning she did for Obama this year helped acquaint her with the gritty rituals of retail politics.
"She's a highly determined woman and she's clearly been thinking about her life and how to make an effective contribution," Klein said. "Everyone knows Caroline, and everyone has a great historical respect for the Kennedy family."
Kennedy is easily the most famous contender for Clinton's seat, but there are plenty of others. New York Attorney General Andrew Cuomo is widely known in the state. Paterson could also pick Buffalo Mayor Byron Brown or Nassau County Executive Tom Suozzi.
There are also a number of House members in the running, including Reps. Carolyn Maloney, Kirsten Gillibrand, Steve Israel, Brian Higgins, Nydia Velazquez and Jerrold Nadler.
Kennedy has strong connections to incoming Obama administration officials - though Obama said he is not going to get involved in New York politics.
As a prominent booster of Obama's presidential bid, Kennedy spent much of 2008 taking bigger steps onto the public stage.
As famous as she is, she always has been viewed as almost painfully shy.
She met her husband, Edwin Schlossberg, while working at the Metropolitan Museum of Art. They married in 1986 and have three children.
She made a splash in early 2008 by writing an op-ed column for The New York Times declaring her support for Obama, saying he had the potential to be as inspirational to Americans as her father was in the 1960s. She also spoke at the Democratic National Convention.
She then hit the campaign trail with Obama and worked on the vice-presidential search that eventually settled on Joe Biden.
Republicans wasted no time in criticizing Kennedy as unqualified for the job and unfamiliar with the state.
"If anything, it makes me more determined to run," said Rep. Peter King, a Long Island Republican who has already expressed his interest in the seat.
"As far as record of achievement I strongly believe that I'm much more qualified, much more experienced, and have an independent record," said King. "Nothing against Caroline Kennedy but I don't think anyone has a right to a seat."
